Existence theorems for some elliptic systems.
On the mean value property of superharmonic and subharmonic functions.
Unique solvability for a second order nonlinear system via two global inversion theorems.
Existence and uniqueness of solutions for a semilinear elliptic system.
Existence of solutions for a system of elliptic partial differential equations.
Le problème de Pompeiu
Positive solutions of nonlinear elliptic systems
We study the existence and nonexistence of positive solutions of nonlinear elliptic systems in an annulus with Dirichlet boundary conditions. In particular, a priori bounds are obtained. We also study a general multiple linear eigenvalue problem on a bounded domain.
Un résultat sur les fonctions de classe et application au problème de Cauchy
Nous montrons principalement que, si est une fonction différentiable sur un intervalle , si sa dérivée est höldérienne d’ordre avec et si (resp. quand (resp. alors , qui est absolument continue, admet (presque partout) une dérivée bornée presque partout.
Uniqueness of positive solutions of nonlinear second order systems.
In this paper we discuss the uniqueness of positive solutions of the nonlinear second order system -u'' = g(v), -v'' = f(u) in (-R,R), u(±R) = v(±R) = 0 where f and g satisfy some appropriate conditions. Our result applies, in particular, to g(v) = v, f(u) = u, p > 1, or f(u) = λu + au + ... + au, with p > 1, a > 0 for j = 1, ..., k and 0 ≤ λ < μ where μ = π/4R.
Positive radial solutions for semilinear biharmonic equations in annular domains.
Un problème de symétrie pour une équation biharmonique
A uniqueness result for an inverse problem
We establish a uniqueness result for an overdetermined boundary value problem. We also raise a new question.
On the mean-value property of superharmonic functions
We complement a previous result concerning a converse of the mean-value property for smooth superharmonic functions. The case of harmonic functions was treated by Kuran and an improvement was given by Armitage and Goldstein.
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